The US State Department's deputy spokesman, Mark Toner, said the Namazis had been "unjustly detained" in Iran, and called for their immediate release.

The detentions come amid an intensifying crackdown against Iranians with ties to the west, directed by powerful hardliners in judiciary and security forces in the aftermath of Iran's historic nuclear deal with the United States and other world powers last year.

Washington and Tehran have not had formal diplomatic relations since the 1979 Islamic revolution that toppled the US-backed shah.

Babak Namazi, Siamak's brother and Baquer's son, said the sentences were unjust.

"My father has been handed practically a death sentence," he said in a statement.

Baquer has a serious heart condition and requires special medication, his wife wrote on Facebook in February.

In a statement released on Tuesday, UNICEF highlighted the Baquer's work in Somalia, Egypt and Kenya, expressing concern for his health and appealing for his release on "humanitarian grounds".

Siamak, who was born in Iran and educated in the US, worked as a business consultant in Iran for several years.

Detente alarms hardliners

Mizan, the Iranian judiciary's official news site, published on Sunday video images of Siamak, set to dramatic music and spliced together with images of US President Barack Obama and Washington Post reporter Jason Rezaian, who was released from an Iranian jail in January after more than 18 months in detention.

Tehran's deal with world powers lifted most international sanctions and promised Iran's reintegration into the global community in exchange for curbs on its nuclear programme.

The potential detente with the west has alarmed Iranian hardliners, who have seen a flood of European trade and investment delegations arrive in Tehran to discuss possible deals, according to Iran experts.

Security officials have arrested dozens of artists, journalists and businessmen, including Iranians holding joint American, European or Canadian citizenship, as part of a crackdown on "western infiltration".

On its Persian-language news site, Fars named the other four sentenced on Monday as Farhard Abdulsaleh, Kamran Qaderi, Nezar Zakka and Alireza Omidvar. Zekka has been previously identified as a US resident from Lebanon. No further details can be released, prosecutor Jafari Dolatabadi told Fars.